caa a22 4500 606166211 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10440-014-9984-y doi (NATIONALLICENCE)springer-10.1007/s10440-014-9984-y Analysis ℓ 1-recovery with Frames and Gaussian Measurements [Elektronische Daten] [Maryia Kabanava, Holger Rauhut] This paper provides novel results for the recovery of signals from undersampled measurements based on analysis ℓ 1-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery guarantees for cosparse (analysis-sparse) signals using Gaussian random measurement matrices. The nonuniform result relies on a recovery condition via tangent cones and the uniform recovery guarantee is based on an analysis version of the null space property. Examining these conditions for Gaussian random matrices leads to precise bounds on the number of measurements required for successful recovery. In the special case of standard sparsity, our result improves a bound due to Rudelson and Vershynin concerning the exact reconstruction of sparse signals from Gaussian measurements with respect to the constant and extends it to stability under passing to approximately sparse signals and to robustness under noise on the measurements. Springer Science+Business Media Dordrecht, 2014 Compressive sensing nationallicence ℓ 1-minimization nationallicence Analysis regularization nationallicence Frames nationallicence Gaussian random matrices nationallicence Kabanava Maryia Lehrstuhl C für Mathematik (Analysis), RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany aut Rauhut Holger Lehrstuhl C für Mathematik (Analysis), RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany aut Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 173-195 0167-8019 140:1<173 2015 140 10440 https://doi.org/10.1007/s10440-014-9984-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9984-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kabanava Maryia Lehrstuhl C für Mathematik (Analysis), RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany aut NATIONALLICENCE 700 1- Rauhut Holger Lehrstuhl C für Mathematik (Analysis), RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 173-195 0167-8019 140:1<173 2015 140 10440